Firstly I am no Pro and this is my first published guide (N.B. This is a serious build, but may be for less serious players). I am currently Silver III and have decided to try and reach Gold by the end of the season, my current main being Janna, with a 100% win ratio.

(and 8 games played)

I first began using a build similar to this when I was trying to learn to play Vayne, I was so bad at laning without someone to peel for me that my opponents often got pretty fed. I used a build similar to this, and by hiding and farming till I could complete most of my build I would almost always make a comeback in the late game, and could 1v1 the opponent I had previously fed in lane.

I have always been a fan of non-meta champions and builds, a particular favorite of mine being AD Twisted Fate. This lead me to trying to find a build that worked for him after Riot removed the CDR from his E, replacing it with extra Attack Speed instead (A buff for AD TF). After feeding in my first few games using a variety of builds from other ADCs I decided to try my 'late game' vayne build, 'late game' being an excuse to suck horribly in lane. I found it fitted TF better than Vayne and in my opinion is a legitimate build for AD TF (though the feeding parts can be taken out at the user's preference).

This build focuses on TF's place as the ADC with the longest and most reliable single target stun in the game. (ADC in this case including anyone ranged with either AD scaling abilities or a form of steroid/on hit effect)

TF's Yellow Card is a guaranteed stun for 2 full seconds which also keeps the enemy in your auto attack range unlike Vayne's Condemn which not only knocks your target away, but also only stuns if they hit a wall, and even then only for 1.5 seconds.

The build, therefore is based on winning a 1v1 with any opponent you encounter within that 2 seconds whether that be killing an enemy squishy or beating a tankier foe to the point that they can only run.

The focus on Tf's Yellow Card could open him up to ambushes from, say, a rengar ultimate, however with good vision and awareness you will hopefully be able to either get a teammate to be ready to peel for you like any other ADC OR, being TF you could simply use your ult to see anyone coming and kill them before they got close.

Pros

High Crit Chance of 90%
Crits of over 600
High Attack Speed
High Movement Speed
BOTRK Active for Damage/Healing/Slow/MoveSpeed
Extra gold income from Avarice Blade+TF Passive

Cons

Under 1.9k HP
Only 5% Lifesteal for most of the game and 19% total
No Armour/MR besides Runes
Only 125 bonus AD from items
Weak until well into the game

This build is not for the conventional. It is for people who don't mind sucking for most of a game, only to then get an unofficial penta before pushing to win. Also a good team helps as it will be a 4v5 for a while if you don't do so well early on.

Once in lane, try to farm and avoid trades remembering your low attack range and AP scaling abilities.
If you get caught overextending, run for your tower and try to stun/slow the enemies.
Don't expect to be flawless by the time your tower dies and don't expect first blood.

Your goal is to survive and to farm. If you are losing trades with the enemy ADC or are being zoned hard, losing your tower will actually help you out a bit.

For your items, start with a Dorans Blade, or whatever you prefer so long as it's not a longsword, then try to get an Avarice Blade and Berserker Greaves by your 1st B or after a couple of deaths.

Hopefully by this point you will have your Avarice Blade and can start raking in the Gold from it and your passive to buy your two Zeals and later a Pickaxe.
Don't get drawn into ulting for kills willy nilly, you can't burst like an AP TF, (Yet).
You should try to stay in a lane safely farming it, leaving buffs, dragon, teamfights, and pushing/defending to your teammates. Though if you already have some strong items and didn't lose lane you should play more like a standard ADC would at this point, although it's not the real point of the build.
Once you can afford your Infinity Edge you're nearly there.

Now you need to get your Statikk Shiv and Phantom Dancer ASAP. You might even be level 18, in which case you should try to split push away from your team to draw a squishy carry over to stop you (retreat from anything too difficult with your ult before they get close).
Wait in a bush or out of range until they are almost close enough, then get your yellow card and right click them, GG. If they have a banshees use your Q to remove it first, if they are too tanky to kill very fast run with your ult beforehand as mentioned above and if they survive on low hp pop your barrier and trade to finish them.
If you've played as I intend this build to be used you should get a juicy 500g shutdown on some very-fed-full-damage-building-overconfident carry.
Once you are back in base buy a Vampiric Sceptre and then either go back to farming in your team doesn't especially need you or join in and do some teamfights. Either way, work towards your Blade of the Ruined King which should allow you to 1v1 most people (Melting Udyrs before they even get close).
I suggest a Yomuu's Ghostblade as your final item for using its active for the movement speed or for the burst with your Gold Card, but a defensive item like Guardian Angel or armor pen or whatever you feel you need most can fill the slot instead. I prefer Distortion for the boots enchant but any of Alacrity, Furor or Homeguard are also viable.

More sections to come & some revisions too
Released early due to peer pressure.

Moldy TF guide by Ylarr